A Markov Additive Risk Process with a Dividend Barrier

A Markov Additive Risk Process with a Dividend Barrier

We study a risk process with dividend barrier b where the claims arrive according to a Markovian additive process (MAP). For spectrally negative MAPs, we present linear equations for the expected discounted dividends and the expected discounted penalty function. We apply results for the first exit t...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Advances in applied probability 2013-06, Vol.45 (2), p.451-489
1. Verfasser: Frostig, Esther
Format: Artikel
Sprache:eng
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 489
container_issue 2
container_start_page 451
container_title Advances in applied probability
container_volume 45
creator Frostig, Esther
description We study a risk process with dividend barrier b where the claims arrive according to a Markovian additive process (MAP). For spectrally negative MAPs, we present linear equations for the expected discounted dividends and the expected discounted penalty function. We apply results for the first exit times of spectrally negative Lévy processes and change-of-measure techniques. Explicit expressions are given when there are positive and negative claims, with phase-type distribution.
doi_str_mv 10.1017/S0001867800006406
format Article
fullrecord <record><control><sourceid>crossref</sourceid><recordid>TN_cdi_crossref_primary_10_1017_S0001867800006406</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>10_1017_S0001867800006406</sourcerecordid><originalsourceid>FETCH-LOGICAL-c856-e19e8626381d3f1d863d634a82b5a602dac7f19cc418cf86d559779f6f26b8a43</originalsourceid><addsrcrecordid>eNplj81KxDAUhYMoWEcfwF1eIJrbNDe3yzr-woiisy-Z_GActZIMFd_eFt25Onx8hwOHsVOQZyDBnD9LKYHQ0JQSG4l7rILGaIET7bNq1mL2h-yolNcJ1dStGHb83ubtMPLO-7RLY-BPqWz5Yx5cKIV_pd0Lt_wyjcmHD88vbM4p5GN2EO1bCSd_uWDr66v18lasHm7ult1KONIoArSBsEZF4FUET6g8qsZSvdEWZe2tMxFa5xogFwm91q0xbcRY44ZsoxYMfmddHkrJIfafOb3b_N2D7Off_b_f6gd6AkjO</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>A Markov Additive Risk Process with a Dividend Barrier</title><source>Jstor Complete Legacy</source><source>Cambridge Journals</source><source>JSTOR Mathematics &amp; Statistics</source><creator>Frostig, Esther</creator><creatorcontrib>Frostig, Esther</creatorcontrib><description>We study a risk process with dividend barrier b where the claims arrive according to a Markovian additive process (MAP). For spectrally negative MAPs, we present linear equations for the expected discounted dividends and the expected discounted penalty function. We apply results for the first exit times of spectrally negative Lévy processes and change-of-measure techniques. Explicit expressions are given when there are positive and negative claims, with phase-type distribution.</description><identifier>ISSN: 0001-8678</identifier><identifier>EISSN: 1475-6064</identifier><identifier>DOI: 10.1017/S0001867800006406</identifier><language>eng</language><ispartof>Advances in applied probability, 2013-06, Vol.45 (2), p.451-489</ispartof><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c856-e19e8626381d3f1d863d634a82b5a602dac7f19cc418cf86d559779f6f26b8a43</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27901,27902</link.rule.ids></links><search><creatorcontrib>Frostig, Esther</creatorcontrib><title>A Markov Additive Risk Process with a Dividend Barrier</title><title>Advances in applied probability</title><description>We study a risk process with dividend barrier b where the claims arrive according to a Markovian additive process (MAP). For spectrally negative MAPs, we present linear equations for the expected discounted dividends and the expected discounted penalty function. We apply results for the first exit times of spectrally negative Lévy processes and change-of-measure techniques. Explicit expressions are given when there are positive and negative claims, with phase-type distribution.</description><issn>0001-8678</issn><issn>1475-6064</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><recordid>eNplj81KxDAUhYMoWEcfwF1eIJrbNDe3yzr-woiisy-Z_GActZIMFd_eFt25Onx8hwOHsVOQZyDBnD9LKYHQ0JQSG4l7rILGaIET7bNq1mL2h-yolNcJ1dStGHb83ubtMPLO-7RLY-BPqWz5Yx5cKIV_pd0Lt_wyjcmHD88vbM4p5GN2EO1bCSd_uWDr66v18lasHm7ult1KONIoArSBsEZF4FUET6g8qsZSvdEWZe2tMxFa5xogFwm91q0xbcRY44ZsoxYMfmddHkrJIfafOb3b_N2D7Off_b_f6gd6AkjO</recordid><startdate>201306</startdate><enddate>201306</enddate><creator>Frostig, Esther</creator><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>201306</creationdate><title>A Markov Additive Risk Process with a Dividend Barrier</title><author>Frostig, Esther</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c856-e19e8626381d3f1d863d634a82b5a602dac7f19cc418cf86d559779f6f26b8a43</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Frostig, Esther</creatorcontrib><collection>CrossRef</collection><jtitle>Advances in applied probability</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Frostig, Esther</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A Markov Additive Risk Process with a Dividend Barrier</atitle><jtitle>Advances in applied probability</jtitle><date>2013-06</date><risdate>2013</risdate><volume>45</volume><issue>2</issue><spage>451</spage><epage>489</epage><pages>451-489</pages><issn>0001-8678</issn><eissn>1475-6064</eissn><abstract>We study a risk process with dividend barrier b where the claims arrive according to a Markovian additive process (MAP). For spectrally negative MAPs, we present linear equations for the expected discounted dividends and the expected discounted penalty function. We apply results for the first exit times of spectrally negative Lévy processes and change-of-measure techniques. Explicit expressions are given when there are positive and negative claims, with phase-type distribution.</abstract><doi>10.1017/S0001867800006406</doi><tpages>39</tpages><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0001-8678
ispartof Advances in applied probability, 2013-06, Vol.45 (2), p.451-489
issn 0001-8678
1475-6064
language eng
recordid cdi_crossref_primary_10_1017_S0001867800006406
source Jstor Complete Legacy; Cambridge Journals; JSTOR Mathematics & Statistics
title A Markov Additive Risk Process with a Dividend Barrier
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-30T11%3A25%3A37IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-crossref&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=A%20Markov%20Additive%20Risk%20Process%20with%20a%20Dividend%20Barrier&rft.jtitle=Advances%20in%20applied%20probability&rft.au=Frostig,%20Esther&rft.date=2013-06&rft.volume=45&rft.issue=2&rft.spage=451&rft.epage=489&rft.pages=451-489&rft.issn=0001-8678&rft.eissn=1475-6064&rft_id=info:doi/10.1017/S0001867800006406&rft_dat=%3Ccrossref%3E10_1017_S0001867800006406%3C/crossref%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true